Is Bitcoin price prediction reliable? EMH theory vs S2F model

Written in front: The original author is PlanB. In this article, he introduced the concepts of the Stock-to-Flow (S2F) model, the efficient market hypothesis (EMH), and the risk and return model. He believes that the market currently overestimates the future Risk, just like in the past 11 years. Therefore, he prefers using the S2F model to predict the future price of Bitcoin, rather than the classic risk and return model.

Black bitcoin coin food concept

(Picture from:

I. Introduction

The Bitcoin Stock-to-Flow (S2F) model was born in March 2019 {{1]}. This model is popular with many Bitcoin enthusiasts and investors. Many analysts have adopted the S2F model and confirmed it with actual Bitcoin price predictions. [2] [3] [4]

Of course, the S2F model has also been criticized. The most representative argument against this model comes from the efficient market hypothesis (EMH). The objection points out that the S2F model is based on publicly available information (S2F, bitcoin's supply trajectory), so analysis and conclusions must have been included in the priced in.

In this article, I share my personal views on S2F models and EMH theory. It then analyzes arbitrage opportunities, risk-reward models, and derivatives markets.

Stock to Flow model

The S2F model was released as a Bitcoin valuation model. It was inspired by the concept of "unforgeable scarcity" proposed by Nick Szabo and the analysis of S2F by Saipedean Ammous [5] [6] .

S2F is a measure of scarcity. Over time, the power-law relationship between S2F and the price of Bitcoin has captured the basic laws of Bitcoin's complex network effect dynamic system described by Trace Mayer [7] .

The S2F model is also a power-law function, which applies to monthly data from October 2009 to February 2019: BTC price = 0.4 * S2F ^ 3 (where S2F = 1 / inflation rate). The other version of the model gives a higher price based on the annual data of 2009-2019: BTC price = 0.18 * S2F ^ 3.3


Nick Phraudsta was the first to validate (or better say "no falsification") the S2F model, and he added co-integration analysis and showed that this correlation may not be false. Marcel Burger validated the S2F model and co-integration, and performed several additional statistical tests.

3. Effective market hypothesis (EMH)

The efficient market hypothesis (EMH) is a well-known theory in financial economics. It is based on the ideas of Friedrich Hayek (Nobel laureate in 1974) and others. According to Hayek, the market is an information processing system that provides the best price discovery possible [8] .

The person who formally proposed the EMH theory was the 2013 Nobel Prize winner Eugene Fama, who described 3 types of EMH [9] :

  1. Weak EMH: Historical price data has been priced in and cannot be used for profit. Technical analysis (TA) and time series analysis (TSA) are ineffective;
  2. Semi-strong EMH: Public news from media and research companies such as MSNBC, Bloomberg, The Wall Street Journal, etc. has been included in the priced in and cannot be used for profit. Basic analysis (FA) does not work;
  3. Strong EMH: Even internal information cannot be used for profit, because all information is priced in.

Most investors and economists agree that modern financial markets are reasonably efficient (ie, they accept weak EMH and semi-strong EMH), but they reject the strong EMH theory .

Then according to EMH theory, the S2F model should be priced in because it is based on publicly available data (S2F).

4. Risk and return models

Honestly, I have never used EMH theory directly in my more than 20 years of institutional investment management (multi-billion euro balance sheet) experience. In practice, we assume EMH and use a risk & reward model.

4.1 Assumed EMH

Some people think that the Bitcoin market is inefficient, but I disagree. In the past, you could buy bitcoins in one dollar for one transaction, sell bitcoins in euros or yen for another, and then convert bitcoins into dollars to make a profit. Arbitrage was possible. But these days have passed, with the prices shown in the table below (20:00 GMT, January 13, 2020):

BTCUSD = 8100

BTCEUR = 7300

BTCUSD / BTCEUR = 8100/7300 = 1.11

EURUSD = 1.11

BTCJPY = 885.000

BTCJPY / BTCUSD = 885.000 / 8100 = 109

USDJPY = 109

If you use mainframe computers, fast communication lines, and high-frequency trading (HFT) algorithms, you may still have some money to make, but this arbitrage opportunity is not so easy to obtain.

We can safely assume that the bitcoin market with a daily transaction volume of US $ 10 billion and a market value of over US $ 150 billion is quite effective.

4.2 Risk and return model

Assuming EMH doesn't mean you can't make money. You just need to take risks. EMH and no arbitrage points lead us to risk and return models.

The 1990 Nobel laureate Harry Markowitz introduced an early risk and return model using his famous portfolio theory (PT) [10] . Another Nobel laureate, William Sharpe, published his famous Capital Asset Pricing Model (CAPM). [11] According to Markowitz and Sharp, all returns can be explained by risk.

This is a simplified version of the risk and reward model:


Picture: Bonds, gold, stocks (1955-2019 data), and Bitcoin (2009-2019 data)

Understanding this chart is very important, so let's dive into it.

The X axis of this chart is risk (maximum annual loss), and the Y axis is return (average annual return).

The chart shows three typical assets: bonds, gold, and stocks. Bonds have the lowest risk (8%) and the lowest return (6%). Gold has a risk of 33% and a return of 7.5%. Stocks have the highest risk (40%) and the highest return (8%).

The key insight is that benefits can be explained by risk alone, which is consistent with EMH. If you come across an asset that is above this line, your first reaction would be: it could be a great investment opportunity. A better response (from the point of view of the efficient market hypothesis and no arbitrage point) is: this is too good, so it cannot be true. We may have missed the risk (or calculated it incorrectly), and we should try to restore the asset to its normal range. Quantifying risk (volatility) is difficult, and in fact this is true for financial institution experts. If an investor calculates that the risk is lower than the market price, and he knows exactly why the performance of the asset is higher than this line, then only then should he decide to invest.

Bitcoin is indeed outside the chart: its return is 200%, and the risk is 80%. Since I couldn't draw it on the chart, I adjusted it to 1% of Bitcoin plus 99% of cash . investment. This Bitcoin investment strategy is also far superior to this line: 8% return, 1% risk (please note that even if Bitcoin falls 99%, your loss will not exceed 1%, because you only invest 1% of funds). So my first reaction was: the market saw a risk not in the data. The following are some possible risks:

  1. Risk of bitcoin death;
  2. The government has made Bitcoin illegal and prosecuted developers for their risks;
  3. Risk of fatal software errors;
  4. Risk of theft of the exchange;
  5. Risk of 51% attack by miners;
  6. Risk of miners falling into a vicious circle after halving;
  7. Hard fork risk

From the perspective of efficient market hypothesis and risk-return theory, all these risks should be included in the price data. But these risks are not in the data. According to the effective market hypothesis and the risk-return formula in the chart, a 1% risk should give a 5.5% + 6.2% * 1% = 5.6% return. The data shows that in the past 11 years, 1% bitcoin + 99% cash has returned 8%.

The market seems to overestimate these risks, and Bitcoin is indeed a huge investment opportunity, which fits the S2F model.

V. Derivatives Market

Regarding the future of the market, let's see what the derivatives market thinks.

The options market does not believe that the price of Bitcoin will rise when or after the next halving:



The futures market is also the same: the price will rise slightly in the future, but there will be no sharp increase when halving or after halving, which means that no special situation will occur when halving:



This is interesting because the S2F model predicts that prices will be much higher after halving. So how do we explain this?

I think the simple answer is that the market is currently overestimating future risks, just as it has been overestimating risks over the past 11 years. An effective bitcoin market not only underestimates the basic value of scarcity (S2F model), but also overestimates all of these risks:


  1. 42% of investors consider bitcoin futures to be the biggest risk (whale and large organizations manipulate bitcoin prices);
  2. 16% are still worried that mining companies will surrender after halving;
  3. 15% are worried about the selling pressure from scam projects;
  4. According to my discussions with institutional investors, their biggest concern is that the government has made Bitcoin illegal.
  5. Another risk often mentioned by institutional investors is "the next bitcoin", a new (government / central bank-backed) currency that will replace bitcoin;

Please note that without these risks, the value of Bitcoin will be much higher than it currently is and may fit the S2F model.

Over time, some of these risks will disappear from the list above. Take the surrender of miners as an example. I don't think that the surrender of miners is a big risk, but 15% of investors think it is a risk. If the computing power does not decrease after the next halving, then the risk of miners surrender will disappear, and the price of Bitcoin will rise because the risk disappears.

6. Conclusion

The Bitcoin S2F model was proposed in March 2019, and it has been verified by many people.

The EMH theory means that the S2F and model predictions should have been priced in by the market in advance, because the S2F model uses public S2F data.

The current Bitcoin market is indeed quite efficient, as there is no chance of easy arbitrage.

Historical risk and return data for bonds, gold, stocks, and bitcoin indicate that the bitcoin market is overestimating risk. Bitcoin's returns do not match the risks, but they fit well with the S2F model. The Bitcoin options and futures market does not expect that the price of Bitcoin will rise when or after the next halving, and the market may still overestimate future risks.

My conclusion is that the Bitcoin market is indeed quite efficient in the S2F model, but it also overestimates the risks. Therefore, I prefer to use the S2F model to predict the future price of Bitcoin, rather than the classic risk and return model.

So I assume EMH, and I definitely pick up Bitcoin!

1. PlanB @ 100trillionUSD, Modeling Bitcoin's Value with Scarcity, Mar 2019 ↵

2. Nick Phraudstra, Falsifying Stock-to-Flow As a Model of Bitcoin Value, Aug 2019 ↵

3. Marcel Burger, Reviewing “Modelling Bitcoin's Value with Scarcity”, Sep 2019 ↵

4.Mannuel Andersch (BayernLB), Is Bitcoin outshining gold ?, Sep 2019 ↵

5. Nick Szabo, Bit Gold, 2008 ↵

6.Saifedean Ammous, The Bitcoin Standard: The Decentralized Alternative to Central Banking, 2018 ↵

7. Trace Mayer, The Seven Network Effects of Bitcoin, 2015 ↵

8. Friedrich Hayek, The Use of Knowledge in Society, 1945 ↵

9. Eugene Fama, Efficient Capital Markets: A Review of Theory and Empirical Work, 1970 ↵

10.Harry Markowitz, Portfolio Selection, 1952 ↵

11. William Sharpe, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, 1964 ↵